The electron emission originating from the surface of a thermoionic electron emitter strongly depends on the “pulling” electric field which is usually generated by the X-ray tube's anode. For enabling fast on/off switching, it is known from the relevant prior art that X-ray tubes of the rotary-anode type may be equipped with a grid electrode placed in the vicinity placed in front of the tube cathode's electron emitter. In ancient radio tubes, said grid electrode was realized as a grid of wires. Therefore, this electrode is still called “grid” despite it looks rather aperture-like in modern X-ray tubes and is a part of the electrostatic focusing of the cathode cup. To shut off the electron beam completely, a so-called cut-off voltage Uco is applied to the grid electrode which generates a repelling field and is usually given by the absolute value of the potential difference between the electron emitter and the grid electrode. The resulting electric field at the emitter surface is the sum of the grid and the anode generated field. If the total field is repelling on all locations on the electron emitter, electron emission is completely cut off.